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Once upon a time, it was possible to install Linux distributions (or another OS) on the PS3, and if you did that it was possible to install Firefox as well. However, Sony removed that option in firmware revision 3.21. Since that time, the only software that can be run on the PS3 is official Sony and Sony licensed software.

Since then, the PS3's security and anti-tampering systems have been broken, and it is possible to put different firmware on your PS3. Doing so likely voids the manufacturer's warranty and you may lose or be locked out of certain console features. However, I believe it may be possible to install Firefox if you were to change the firmware.

I don't have any reliable links for this sort of information, as it's hard to authenticate these kind of sites. Additionally, I don't want to provide information that may lead to you damaging your console. I'm only mentioning this to provide a complete answer, and I strongly suggest you leave your PS3's firmware alone.